MATH 240 Midterm: MATH240 spring2007M2 math232 solution

• School: Simon Fraser University
• Department: Mathematics
• Course: MATH 240
• Professor: All

Document Summary

Math 232 first midterm solution february 5, 2007: we consider the following system of equations: x1 +x2 +2x3 4x4 = 1 x1 +2x2 +x3 +x4 = 2. 2x1 +4x2 +2x3 x4 = 1 (a) (1 point) write down the augmented matrix corresponding to this system. 2 4 2 1 1 (b) (3 points) determine the reduced row echelon form of this matrix. Show your work. (use the back of the previous page if you need more room) Page 2 of 5 (c) (2 points) write down the full solution set to the system in parametric form. From part (b) we see that the given system is equivalent to x1 = 9 3x3 x2 = 4 + x3 x3 x4 = 1 free variable. Hence, in parametric form, the set of solution vectors is: x1 x2 x3 x4. 0 (d) (2 points) let b = . Can you write b as a linear combination of a1, .